sara seager - lecture2 - mit
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TRANSCRIPT
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TrentSchindler
TrentSchindler
Sara Seager Massachusetts
Institute of Technology
Exoplanet Mass and Radius and the Physics of Planetary Interiors
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CaseyReid
Planet Interiors
The goal is to constrain the interior composition of exoplanets by their mass and radius measurements
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Planet Mass-Radius 1995
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Planet Mass-Radius 2000
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Planet Mass-Radius 2005
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Planet Mass-Radius 2010
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Exoplanet Interiors Introduction Mass-Radius Relationships
Two Transiting Super Earths Kepler and Beyond
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Exoplanet Mass-Radius Diagram Aimtoinferanexoplanet’sbulkcomposi<onfromitsMandR
Seager et al. 2007
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Seager,Kuchner,Hier‐Majumder,Militzer2007ZapolskyandSalpeter1969Stevenson1982,Hubbard1984Valenciaetal.2006,2007So<netal.2007Selsisetal.2007…andothers
Weinferanexoplanet’sbulkcomposi<onfromitsMandR
€
dP(r)dr
=−Gm(r)ρ(r)
r2
ρ(r) = F(P(r),T(r))€
dm(r )dr
= 4πr 2ρ(r )
Exoplanet Mass-Radius Diagram
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Equation of State
Describesrela<onshipbetweendensity,temperatureandpressureforamaterialinthermodynamicequilibrium
1) Idealgaslaw:P=nkT;ρ=PmHµ/kT2) Polytrope:P=Kρ(n+1)/n3) VinetEOS
€
ρ(r) = f T(r),P(r)( )
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High Pressure Physics Experiments
Wikipedia
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Mass-radius relationships appear have a common functional form
Exoplanet Mass-Radius Diagram
Seager et al. 2007
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Equation of State
Ms<~4
Ms<<1
€
log10 Rs = −0.209 +1/3log10 Ms − 0.0804 ×Ms0.394
Seageretal.2007
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Equation of State
Overall,theEOSsapproximatelyfollowρ=ρ0+cPnA“modifiedpolytrope”Ms<~4
Ms<<1
€
log10 Rs = −0.209 +1/3log10 Ms − 0.0804 ×Ms0.394
Seageretal.2007
Thomas‐Fermi‐DiracEOS
VinetEOS
NosimpleEOSformula<onforpressuresbetweenVinetandTFD
Seager et al. 2007
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€
Ms =43πRs
3 1+ 1− 35n
23πRs
2
n
Ms<~4
Ms<<1
€
log10 Rs = −0.209 +1/3log10 Ms − 0.0804 ×Ms0.394
Seageretal.2007
€
dm(r)dr
= 4πr2ρ(r)
€
dP(r)dr
=−Gm(r)ρ(r)
r2
ρ(r) = ρ0 + cP(r)n
The mass-radius relationships for cold terrestria lmass planets follow a generic functional form because the EOS are well approximated by a modified polytrope.
Generic Mass-Radius Relation
Seager et al. 2007
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DiversityofsuperEarths?
Waterplanets?
Neptune‐sizebutnotnecessarilyicegiants
Currentground‐basedtransitsurveys.Someplanetsaretoobig!
Seager et al. 2007
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Mass-Radius Relation Summary
Mass‐radiusrela<onshipsarewellunderstoodbutarenotadequatetostudy
individualobjects.
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Exoplanet Interiors Introduction Mass-Radius Relationships
Two Transiting Super Earths
Kepler and Beyond
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Planet Interiors
Exoplanets can be composed of three (or four) materials: rock (and iron), ice, and gas RogersandSeager2010b;Chambers2010
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Ternary Diagrams
hgp://csmres.jmu.edu/geollab/fichter/SedRx/readternary.html
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Ternary Diagrams
hgp://csmres.jmu.edu/geollab/fichter/SedRx/readternary.html
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Ternary Diagrams
hgp://csmres.jmu.edu/geollab/fichter/SedRx/readternary.html
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Ternary Diagrams
ZengandSeager2008
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CoRoT‐7b
The first transiting super Earth R = 1.68±0.09 R M = 4.8±0.8 M P = 0.85 days a = 0.017 AU T ~ 2500 K
Leger et al. 2009 Queloz et al. 2009
RogersandSeager2010b
Degeneracy in internal composition is a permanent limitation no matter how small the observational uncertainties
Ternary diagrams: see Valencia et al. 2007 Zeng & Seager 2008
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CoRoT‐7b
RogersandSeager2010b
R = 1.68±0.09 REarth M = 4.8±0.8 MEarth
CoRoT-7b is likely made of material less dense than Earthʼs, assuming no water content
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GJ 1214b
GJ 1214b by Charbonneau et al. 2009 Interpretation by Rogers and Seager 2010a
The second transiting super Earth R = 2.68±0.13 R M = 6.6±0.8 M P = 1.58 days a = 0.014 AU T ~ 550 K
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Quaternary Diagrams
Most super Earths or exo-Neptunes found in the near future are likely to have gas envelopes.
This adds a further degeneracy to the interior composition interpretation.
Adds more complexity t the models because of the free parameters in the gas layer.
RogersandSeager2010b
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GJ 1214b
GJ 1214b by Charbonneau et al. 2009 Interpretation by Rogers and Seager 2010a
The second transiting super Earth R = 2.68±0.13 R M = 6.6±0.8 M P = 1.58 days a = 0.014 AU T <~ 550 K
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Water Phase Diagram 1012
106
103
1
109
Pressure(P
a)
Temperature(K)0 200 400 800600
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Super Earth Interiors Summary Interiorcomposi<oninterpreta<onishighly
degeneratebasedonmassandradiusmeasurements
Parameterspacecanbequan<ta<velyconstrained,andcri<calinterpreta<oncans<llbemade,e.g.,the
likelyabsenceofliquidwateronGJ1214b
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Exoplanet Interiors Introduction Mass-Radius Relationships
Two Transiting Super Earths Kepler and Beyond
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NASAʼs Kepler Space Telescope
Telescope Summary 0.95 m 105 sq-degree FOV Centered in the Cygnus-Lyra region No moving parts in science payload Heliocentric Earth-trailing orbit Telemetry limited Bandpass 423-897 nm
Goal: to determine the frequency of Earth-size planets in Earth-like orbits about sun-sized stars
Boruckietal.2010
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Planets 2000
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Planets 2005
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Planets June 14 2010
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Planet Candidates June 15 2010
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Planet Candidates June 15 2010
Too faint for RV followup About ½ false positives
See Borucki et al. 2010, astroph yesterday
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Astrophysical False Positives
• Eclipsing binary with grazing orientation
• Small star crossing in front of another star
• Eclipsing binary diluted by the light of a third star (“blend”): the trickiest case
AdaptedfromG.Torres
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Number of Planet Candidates
Boruckietal.2010
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Planet Candidates vs. Semi-Major Axis
Boruckietal.2010
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Kepler Multi-Planet Transits
Five multi-planet candidate systems were announced yesterday Steffen et al. astroph yesterday
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Multi-Planet Transits Harbinger for huge advancements in exoplanet science Planet formation -why so coplanar? -frequency of coplanar systems?
Orbital evolution -orbital resonances
Planet characterization -masses (from transit timing variations) and radii for planets in the same system
V = 13.9 R = 0.58 RJ P > 27 d
R = 0.3 RJ P = 27.406 d
R = 0.3 RJ P = 13.478 d
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KeplerSummaryKeplerwillmorethandoublethenumberofexoplanets,extendingtheorbitalsepara<onoftransi<ngplanetsout
to1AU.Thedatareleaseisagame‐changerforexoplanetscience
intermsofquan<tyvs.detailedphysicalproper<es
Theplanistoconnectradiivs.periodwithplanetinteriorsandpopula<onsynthesismodelstoconstrain
planetforma<onmodels
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Ultimately we want to connect planet atmosphere and interior models with planet formation and population synthesis models and large observational data sets like Kepler.
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Summary • Mass-Radius Measurements
– For almost 100 exoplanets – Mass-radius relationships are well understood
• Characterization of Individual Super Earths – Only two data points (mass and radius) translates to a
permanent degeneracy in interior composition – Quantitative constraints are possible
• Kepler Data – Historic announcement of 5 multi-planet transiting candidates – Hundreds of new planet candidates
• The Way Forward – connect mass, radius, and/or period data, planet population
synthesis models, and planet interior and atmosphere models – With the aim of understanding planet formation, migration, and
evolution